U.S. patent number 8,636,061 [Application Number 12/668,224] was granted by the patent office on 2014-01-28 for tool for downhole formation evaluation.
This patent grant is currently assigned to Schlumberger Technology Corporation. The grantee listed for this patent is Ollivier Faivre, Mehdi Hizem, Laurent Mosse, Matthieu Simon. Invention is credited to Ollivier Faivre, Mehdi Hizem, Laurent Mosse, Matthieu Simon.
United States Patent |
8,636,061 |
Mosse , et al. |
January 28, 2014 |
Tool for downhole formation evaluation
Abstract
An apparatus for determining a property of a downhole formation,
the apparatus comprising: an array having a plurality of
transmitters and receivers capable of propagating electromagnetic
waves through the formation; measuring circuitry for measuring an
effect of the formation on the propagating waves; control circuitry
arranged to vary the propagating waves as a function of at least
one of frequency, spacing and polarization; and processing
circuitry arranged to combine the effects of the propagating waves
that are varied according to frequency, spacing and polarization
for determining the property of the downhole formation.
Inventors: |
Mosse; Laurent (Montrouge,
FR), Simon; Matthieu (Princeton, NJ), Faivre;
Ollivier (Paris, FR), Hizem; Mehdi (Paris,
FR) |
Applicant: |
Name |
City |
State |
Country |
Type |
Mosse; Laurent
Simon; Matthieu
Faivre; Ollivier
Hizem; Mehdi |
Montrouge
Princeton
Paris
Paris |
N/A
NJ
N/A
N/A |
FR
US
FR
FR |
|
|
Assignee: |
Schlumberger Technology
Corporation (Sugar Land, TX)
|
Family
ID: |
39406135 |
Appl.
No.: |
12/668,224 |
Filed: |
June 6, 2008 |
PCT
Filed: |
June 06, 2008 |
PCT No.: |
PCT/EP2008/004677 |
371(c)(1),(2),(4) Date: |
August 23, 2010 |
PCT
Pub. No.: |
WO2009/006975 |
PCT
Pub. Date: |
January 15, 2009 |
Prior Publication Data
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|
|
|
Document
Identifier |
Publication Date |
|
US 20100307741 A1 |
Dec 9, 2010 |
|
Foreign Application Priority Data
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|
|
|
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Jul 12, 2007 [EP] |
|
|
07112397 |
|
Current U.S.
Class: |
166/250.01;
324/323 |
Current CPC
Class: |
G01V
3/30 (20130101) |
Current International
Class: |
G01V
3/30 (20060101); E21B 47/00 (20120101) |
Field of
Search: |
;166/250.01,66
;324/338,341,343,367 ;367/25 ;703/2 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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0869376 |
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Oct 1998 |
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EP |
|
1 435 639 |
|
Jul 2004 |
|
EP |
|
1693685 |
|
Aug 2006 |
|
EP |
|
11-096921 |
|
Apr 1999 |
|
JP |
|
2002-203487 |
|
Jul 2002 |
|
JP |
|
2002-324488 |
|
Nov 2002 |
|
JP |
|
1999-0056758 |
|
Jul 1999 |
|
KR |
|
10-2002-0026040 |
|
Apr 2002 |
|
KR |
|
10-2004-0058566 |
|
Jul 2004 |
|
KR |
|
10-2004-0062381 |
|
Jul 2004 |
|
KR |
|
Other References
European Office Action of the European Patent Application No. 05 11
0284, mailed on Apr. 6, 2006. cited by applicant.
|
Primary Examiner: Stephenson; Daniel P
Attorney, Agent or Firm: Chi; Stephanie DeStefanis; Jody
Claims
The invention claimed is:
1. An apparatus for determining a property of a downhole formation,
the apparatus comprising: an array having a plurality of
transmitters and receivers capable of propagating electromagnetic
waves through the formation; measuring circuitry for measuring an
effect of the formation on the propagating waves; control circuitry
arranged to vary the propagating waves as a function of frequency,
spacing and polarization; and processing circuitry arranged to
combine the effects of the propagating waves that are varied
according to frequency, spacing and polarization for determining
the property of the downhole formation.
2. The apparatus of claim 1, wherein the simultaneous combination
of the measured effects of varied frequency, spacing and
polarization enable a plurality of different volumes of the
formation to be scanned simultaneously.
3. The apparatus of claim 1, wherein the effects of a plurality of
varied frequencies, spacing and polarization are combined
simultaneously.
4. The apparatus of claim 1, wherein the control circuitry having a
frequency generator for varying the propagating waves.
5. The apparatus of claim 1, wherein the spacing is varied by at
least one of selecting transmitters and receivers in the array that
are spaced at varied distances relative to each other.
6. The apparatus of claim 1, wherein the array is capable of
varying the polarization to be at least one of transversal and
longitudinal polarization by feeding a current through at least two
collocated conductors in an antenna cavity of the relevant
transmitter of the array.
7. A method for determining different volumes of a formation
simultaneously, the method comprising: propagating electromagnetic
waves through the formation with an array having a plurality of
transmitters and receivers; measuring an effect of the propagating
waves on the formation; controlling the propagating waves to vary
as a function of frequency, spacing and polarization, each of
varied propagating waves having a different effect on the
formation; and combining the measured effects of the varied
propagating waves for determining different volumes of the
formation simultaneously.
8. The method of claim 7, wherein at least some of the different
volumes of the formation overlap such that it is possible to
combine said overlapping volumes for determining a more accurate
estimation of a property of the formation in the overlapping
volumes.
9. The method of claim 7, where the different volumes of the
formation are different depths of investigation into the formation.
Description
FIELD OF THE INVENTION
The invention relates to an apparatus and method for determining a
property of a downhole formation, and in particular but not
exclusively, for determination rock and/or fluid properties of the
formation.
BACKGROUND OF THE INVENTION
Logging devices which measure formation dielectric constant are
known, for example from U.S. Pat. No. 3,849,721 and U.S. Pat. No.
3,944,910. The logging device includes a transmitter and spaced
receivers mounted in a pad that is urged against a bore hole wall.
An electromagnetic (EM) microwave is transmitted into the
formations, and the wave which has propagated through the
formations is received at the receiving antennas. The phase shift
and attenuation of this wave propagating in the formations is
determined from the receivers output signals. The dielectric
constant and the conductivity of the formations can then be
obtained from the phase shift and attenuation measurements. Two
transmitters are generally used in a bore hole compensated array to
minimize the effect of bore hole rugosity, tool tilt, and
dissimilarities in the transmitters, receivers, and their
electronic circuits.
These types of probes had limited accuracy, which was improved by
the architectural arrangement described in European Patent
Publication No EP 1 693 685 published on 23 Aug. 2006. This
arrangement proposed the use of a different spacing, frequency or
wave polarization for performing EM measurements of the downhole
formation.
SUMMARY OF THE INVENTION
It is desirable to propose a tool capable of providing even more
accurate downhole measurements.
According to a first aspect of the invention there is provided an
apparatus for determining a property of a downhole formation, the
apparatus comprising: an array having a plurality of transmitters
and receivers capable of propagating electromagnetic waves through
the formation; measuring circuitry for measuring an effect of the
formation on the propagating waves; control circuitry arranged to
vary the propagating waves as a function of at least one of
frequency, spacing and polarization; and processing circuitry
arranged to combine the effects of the propagating waves that are
varied according to frequency, spacing and polarization for
determining the property of the downhole formation.
By combing the different effects simultaneously, the logging tool
of the present invention is able to have more information about the
formation and is therefore advantageously able to provide a more
accurate image of the formation being scanned to the geologist on
the surface. Indeed by combining these three effects
simultaneously, the logging tool offers a cumulative advantage in
increasing the accuracy of different properties of the scanned
formation.
Preferably, wherein the simultaneous combination of the measured
effects of varied frequency, spacing and polarization enable a
plurality of different volumes of the formation to be scanned
simultaneously.
Preferably, wherein the effects of a plurality of varied
frequencies, spacing and polarization are combined
simultaneously.
Preferably, wherein the control circuitry having a frequency
generator for varying the propagating waves (not shown).
Preferably, wherein the spacing is varied by at least one of
selecting transmitters and receivers in the array that are spaced
at varied distances relative to each other.
Preferably, wherein the array is capable of varying the
polarization to be at least one transversal and longitudinal
polarization.
According to a further aspect of the invention there is provided a
method for determining different volumes of a formation
simultaneously, the method comprising: propagating electromagnetic
waves through the formation with an array having a plurality of
transmitters and receivers; measuring an effect of the propagating
waves on the formation; controlling the propagating waves to vary
as a function of frequency, spacing and polarization, each of
varied propagating waves having a different effect on the
formation; and combining the measured effects of the varied
propagating waves for determining different volumes of the
formation simultaneously.
Preferably, wherein at least some of the different volumes of the
formation overlap such that it is possible to combine said
overlapping volumes for determining a more accurate estimation of a
property of the formation in the overlapping volumes.
Preferably, wherein the different volumes of the formation are
different depths of investigation into the formation.
According to a further aspect of the invention there is provided a
method for determining a radial profile of a formation, the method
comprising: scanning the formation with a logging tool located
adjacent a borehole wall of the formation, the logging tool having
a transceiver array for propagating and measuring electromagnetic
effects on the formation; modeling the scanned formation as a
series of layers, the layers being located at respective radial
distances from the borehole wall and wherein each radial layer
being of a predetermined radial length; and determining for each of
the series of layers a respective value of a formation property
using a petrophysical model such that the determined radial profile
is comprised of said respective values of the formation property
that is a petrophysical property.
Preferably, wherein each of the layers having a predetermined
radial length that is thin enough so as to represent the radial
profile as a continuous profile.
According to a further aspect of the invention there is provided a
logging tool for determining a radial profile of a formation, the
logging tool comprising: a transceiver array adjacent a borehole
wall of the formation for scanning the formation by propagating and
measuring electromagnetic effects on the formation; processing
circuitry for modeling the scanned formation as a series of layers,
the layers being located at respective radial distances from the
borehole wall and wherein each radial layer being of a
predetermined radial length, said processing circuitry determining
for each of the series of layers, a respective value of a formation
property using a petrophysical model such that the determined
radial profile is comprised of said respective values of the
formation property that is a petrophysical property.
According to a further aspect of the invention there is provided a
method for measuring a property of a formation, the method
comprising: positioning a logging tool adjacent a borehole wall
with a transceiver array having transmitters and receivers for
propagating and measuring electromagnetic effects in the formation;
selecting at least one transmitter and one receiver to be coupled
together forming a transceiver pair having a single spacing for
propagating and measuring the effects of the formation directly;
and measuring the property of the formation at a distance
substantially near to the borehole wall with the single-spaced
transceiver pair; and compensating for a gain of the single-spaced
transceiver pair to determine the property of the formation.
According to a further aspect of the invention there is provided a
logging tool for measuring a property of a formation, the logging
tool comprising: a transceiver array located adjacent a borehole
wall having transmitters and receivers for propagating and
measuring electromagnetic effects in the formation; selection
circuitry for selecting at least one transmitter and one receiver
to be coupled together to form a transceiver pair having a single
spacing for propagating and measuring the electromagnetic effects
of the formation directly; measuring the property of the formation
at a distance substantially near to the borehole wall with the
single-spaced transceiver pair; and compensating for a gain of the
single-spaced transceiver pair to determine the property of the
formation.
According to a further aspect of the invention there is provided a
logging tool for measuring a property of an anisotropic formation,
the logging tool comprising: a transceiver array located adjacent a
borehole wall having transmitters and receivers for propagating and
measuring electromagnetic effects in the formation; selection
circuitry for selecting at least one transmitter and one receiver
to be coupled together to form a transceiver pair having a single
spacing for propagating and measuring the electromagnetic effects
of the formation directly; and measuring the property of the
anisotropic formation with the single-spaced transceiver pair.
According to a further aspect of the invention there is provided a
method for modeling a logging tool, the method comprising:
generating a tabulated representation of a homogenous pad model,
which models the logging tool as a cylindrical geometrical model
surrounded by a homogeneous formation, the tabulated representation
being a table storing predetermined parameters; generating an
analytical representation of a homogenous plane model, which models
the logging tool as an infinite geometrical plane surrounded by a
homogenous formation; determining the difference between the
tabulated pad model and the analytic plane model to obtain a set of
correction values; and
inverting a set of measured electromagnetic characteristics of a
formation corrected with said set of correction values and using
the non homogeneous plane model
Preferably, wherein the set of measured electromagnetic
characteristics is an attenuation and phase shift measurement.
According to a further aspect of the invention there is provided a
method for modeling a logging tool, the method comprising:
measuring the electromagnetic characteristics of a formation using
a transceiver pad of the logging tool; performing inversion
processing of the measured electromagnetic characteristics based on
a pad model that considers the logging tool to have a cylindrical
cross-sectional shape, wherein the processing associated with the
pad model is reduced by assuming that the formation around the pad
model is homogenous; and representing the pad model as a table
having a plurality of predetermined parameters of the
formation.
According to a further aspect of the invention there is provided a
logging tool for detecting a fracture in a formation, the logging
tool comprising: a transmitter and a receiver spaced at a distance
on a pad of the logging tool for propagating and measuring
electromagnetic effects in the formation; monitoring a response of
the logging tool as the pad is passed over a fracture in the
formation, wherein the response remains constant while the fracture
is located between the transmitter and receiver; and detecting the
fracture from the constant response of the logging tool.
According to a further aspect of the invention there is provided an
imaging system for displaying a property of a formation located
downhole to a user, the system comprising: a logging tool located
substantially adjacent the formation located downhole, the logging
tool comprising a transceiver pad with associate control circuitry
for controlling the propagation and measurement of electromagnetic
effects on the formation; processing circuitry for performing at
least one of the functions: modeling the formation to determine a
petrophysical parameter of the formation directly from the measured
electromagnetic effects, modeling the logging tool as a pad model
with a predetermined parameter table for reducing processing
complexity, using single-spaced transmitter-receiver pairs for
determining a property close to the borehole wall and for an
anisitropic formation, determining the location of a fracture and a
dimension thereof, and the detection of conductive and
non-conductive inclusions in the formation by combing a
longitudinal and transverse polarizations; and a display unit for
displaying the property of the formation based on a result of the
at least one function performed by the processing circuitry.
LIST OF DRAWINGS
Embodiments of the present invention will now be described by way
of an example with reference to the accompanying drawings, in
which:
FIG. 1 shows a an example of a typical onshore hydrocarbon well
location;
FIG. 2 shows a top cross-section view in a geological
formation;
FIG. 3 shows two different profile views of the logging tool
according to one embodiment;
FIG. 4 shows a geometric representation of a transmitter and
receiver defined in space;
FIG. 5 shows a sensitivity response using different spacings;
FIG. 6 shows the integrated response of FIG. 5;
FIG. 7 shows the respective responses using different
frequencies;
FIG. 8 shows the intergrated response of FIG. 7;
FIG. 9 shows a response combining the geometric factor, skin depth
and wave effect terms using different frequencies;
FIG. 10 shows the intergrated response of FIG. 9;
FIG. 11 shows a longitudinal polarization of the logging tool;
FIG. 12 shows a transverse polarization of the logging tool;
FIG. 13 shows an electromagnetic model of the formation according
to one embodiment;
FIG. 14 shows a petrophysical model of the formation according to a
further embodiment;
FIG. 15 shows an example of inversion results and inversion
mismatch using the EM model;
FIG. 16 shows an example of results sensitivies at various
depths;
FIG. 17 shows the petrophysical model automatically linking the
different frequencies;
FIG. 18 shows an example of the results from processing using a
petrophysical model on a field log when using r1=r2;
FIG. 19 shows standard differential measurement;
FIG. 20 shows a non-differential measurement according to a first
embodiment;
FIG. 21 shows two non-differential measurements according a further
embodiment;
FIG. 22 shows an example of graph representing the improvement of
non-differential measurements as compared to a differential
measurement;
FIG. 23 shows a plane model representation;
FIG. 24 shows a cylindrical pad model representation;
FIG. 25 shows a flowchart representing processing steps of a pad
projection model according to an embodiment;
FIG. 26 shows an example of an apparent permittivity comparison
between plane and pad models;
FIG. 27 shows an example of an apparent conductivity comparison
between plane and pad models;
FIG. 28 shows a fracture detected centrally between the flat
responses associated with a plurality of single-spaced
transmitter-receiver pairs at a plurality of frequencies;
FIG. 29 shows an example of a graph according to an embodiment for
determining the fracture thickness;
FIG. 30 shows an example of a graph according to a further
embodiment for determining the fracture thickness;
FIG. 31 shows a first example of a linear dependency on the
fracture thickness;
FIG. 32 shows a further example of a linear dependency on the
fracture thickness;
FIG. 33 shows a flowchart of the processing steps for determining
the thickness of a small fracture according to one embodiment;
FIG. 34 shows an example of graph according to an embodiment for
detecting dip characteristics;
FIG. 35 shows an example of graph where there is no dip;
FIG. 36 shows an example of graphs reflecting imbalance patterns in
the presence of a fracture;
FIG. 37 shows inclusions detected by combining the longitudinal and
transverse polarizations according to one embodiment;
FIG. 38 shows an example of a log display detecting non-conductive
inclusions in a conglomerate formation; and
FIG. 39 shows a graphical representation of various embodiments
being combined for determining an improved radial profile.
DESCRIPTION
FIG. 1 schematically shows a typical onshore hydrocarbon well
location and surface equipments SE above a hydrocarbon geological
formation GF after drilling operation has been carried out. At this
stage, i.e. before a casing string is run and before cementing
operations are carried out, the well-bore is a bore hole WBH filled
with a fluid mixture DM. The fluid mixture DM is typically a
mixture of drilling fluid and drilling mud. In this example, the
surface equipments SE comprises an oil rig OR and a surface unit SU
for deploying a logging tool TL in the well-bore WB. The surface
unit may be a vehicle coupled to the logging tool by a line LN.
Further, the surface unit comprises an appropriate device for
determining the depth position of the logging tool relatively to
the surface level. The logging tool TL may comprise a centralizer.
The centralizer comprises a plurality of mechanical arm that can be
deployed radially for contacting the well-bore wall WBW. The
mechanical arm insures a correct positioning of the logging tool
along the central axis of the well-bore hole. The logging tool TL
comprises various sensors and provides various measurement data
related to the hydrocarbon geological formation GF and/or the fluid
mixture DM. These measurement data are collected by the logging
tool TL and transmitted to the surface unit SU. The surface unit SU
comprises appropriate electronic and software arrangements for
processing, analyzing and storing the measurement data provided by
the logging tool TL.
It should be appreciated that in an alternative embodiment such
processing circuitry is capable of being located downhole in or
near the logging tool TL itself. Such processing circuitry being
capable of handling all the processing functionality pertaining to
the various measurements and models described herein.
Moreover, while FIG. 1 is shown for a wireline application, it
should also be appreciated that the embodiments describe herein are
equally applicable to a logging while drilling application. That
is, there is no need for the logging tool to be limited to an
application wherein it is attached to a separate wire or cable
controlling its movements, it is possible for the different
functionality of the logging tool to be incorporated into the
actual drill pipe itself (for example on the drill collar). This
advantageously allows the benefits of the improved imaging
techniques described herein to be used during the initial drilling
stage as well.
The logging tool TL comprises a probe 1 for measuring the
electromagnetic properties of a subsurface formation according to
the invention. Once the logging tool is positioned at a desired
depth, the probe 1 can be deployed from the logging tool TL against
the bore hole wall WBW by an appropriate deploying arrangement, for
example an arm.
FIG. 2 is a top cross-section view in a geological formation GF.
The bore hole WBH is filled with the fluid mixture DM, generally
drilling fluid and drilling mud. The bore hole wall screens the
particles of mud suspended into the fluid mixture. Thus, a shallow
layer of mud, the so-called mudcake MC is generally formed on the
bore hole wall WBW. A flushed or invaded zone IZ forming a first
concentric volume surrounds the bore hole WBH. The fluid mixture DM
generally filtrates through the mudcake MC and penetrates into the
formation, forming the invaded zone IZ. The radial depth of the
invaded zone varies from a few inch to a few feet. A true or virgin
zone VZ surrounds the invaded zone IZ. It is only filled with the
natural geological formation fluid. A further transition zone may
be present between the invaded zone IZ and the virgin zone VZ.
Therefore, the measurement performed by the logging tool TL are
affected by the presence of the fluid mixture DM into the
geological formation GF, by the size of the invaded zone IZ and by
the presence and size of the mudcake MC.
FIG. 3 shows a two different profile views of the logging tool. The
first profile is viewed as seen from the geological formation,
while the other profile is viewed side-on to the formation showing
the tool aligned adjacent to the MC. The logging tool is shown in
the embodiment of FIG. 3 to comprise two transmitters and eight
receivers distributed axially along a length of the logging tool.
Specifically, there are four receivers located above the upper
transmitter 7, another four receivers 5A, 5B, 6A and 6B located
below the lower transmitter and two further receivers located
between the upper 7 and lower transmitter. The electromagnetic
probe 1 comprises a pad 2. The pad is a conductive metal housing,
for example made in a metallic material like stainless steel. The
pad 2 is coupled to the tool TL by an arm that enables the
deployment of the electromagnetic probe 1, more precisely the pad
2, from the tool TL into the bore hole WBH.
It is possible to configure the two transmitting antennas to define
a central point between them. Each antenna is spaced from a
distance d.sub.0 from the central point. The distance d.sub.0
sensibly defines the electromagnetic probe depth of investigation,
whereas the distance d.sub.1 between the two transmitters sensibly
defines the vertical resolution, for example 1 inch. The eight
receiving antennas can be grouped into sets, for example 4 sets
wherein each set comprising two receiving antennas positioned on
each side of the transmitting antennas. By varying the spacing of
the sets of receiving antennas from the central point it is
possible to vary the depth of investigation of the tool. That is,
the respective sets of receiving antennas, being at different
spacings (from the central points), are able to investigate at
different radial depths into the formation.
Thus, the transmitter/receiver arrangement relies on
electromagnetic wave propagation for measurements. The general
principle of these measurements is to record at a receiver the
voltage induced by a propagating electromagnetic field emitted at a
transmitter.
FIG. 4 shows a basic diagram of the various parameters that may be
defined and derived from such a transmitter-receiver relationship.
The distance between the transmitter and receiver is d. The induced
voltage at the receiver is proportional to the magnetic field at
this receiver if the receiver is a magnetic dipole or proportional
to the electric field if the receiver is an electric dipole. It is
possible to extract from the complex induced voltage, its
logarithmic amplitude and phase that can be expressed as:
Amp+iPha.varies. ln(V).varies. ln(H.sub.R)
The characteristics of the electromagnetic field at the receiver on
the dielectric properties of the surrounding medium can be
described in terms of the relative permittivity .di-elect cons.
(unit-less) and the conductivity .sigma. in Siemens per meter
[S/m]. Both properties can be described as a complex permittivity
expressed:
I.times..sigma..omega. ##EQU00001## where .omega. is the circular
frequency of the electromagnetic wave. The medium propagation
constant is linked to the complex permittivity through
.omega..times. ##EQU00002##
If the medium in not homogeneous, for example if it contains radial
layers, then the measured permittivity and conductivity of the
different spacings, which are bulk quantities, are called apparent
permittivity and apparent conductivity and are functions of the
actual formation properties.
Therefore, various embodiments of the invention are able to take
measurements using electromagnetic waves having different spacings,
frequency and polarization for extracting more accurate radial
information of the borehole characteristics. Specifically, the
amplitudes and phases measurements are obtained from the logging
tool having an array of transmitters and receivers with different
spacings, polarizations and frequencies.
The so-called "forward model" FM is a model that relates the
measured amplitude and phase to the actual properties of the
formation: Amp+iPha=FM(.di-elect cons..sub.1,.di-elect
cons..sub.2,h.sub.1, . . . ), Equation 1 where .di-elect
cons..sub.1,.di-elect cons..sub.2,h.sub.1, are constituent
properties of the formation.
According to one embodiment of the invention, it is possible to
simultaneously combine the data measured at different spacing,
frequency and polarizations to inverse for formation radial
profile. Specifically, each of the different spacing, frequency
measurements has an associated radial response function and the
benefit of combining these radial response functions allows for an
improved characterization of various formation properties, for
example the so-called `standoff` and/or `mudcake` values.
FIG. 4 shows that for a magnetic couple comprising a transmitter
and receiver, in a longitudinal polarization, the sensitivity
function relating the change in induced voltage due to a small
permittivity perturbation at position ({right arrow over (r)})
reads
.GAMMA..function.>.varies..function..rho..DELTA..function..rho..times.-
.PSI..function..rho..PHI..function..rho..times..times..times..PSI..functio-
n..rho..function..times.I.times..times..pi..times..lamda..times..times..DE-
LTA..function..rho..function..delta..times..times..function..rho..rho..tim-
es..times..PHI..function..rho..delta..times..pi..lamda..delta..times..time-
s.I.times..times..pi..lamda..times..times..times..delta..times..times.
##EQU00003##
We call G(.rho., z) the geometrical term, .DELTA.(.rho., z) the
skin depth term, .PSI.(.rho., z) the wave term and finally
.PHI.(.rho., z) the gradient term.
The sensitivity function (Equation 2) is a function of various
terms. The more these terms vary one from the other when different
spacing, frequency and polarization measurements are compared; the
higher the sensitivity and thus the more accurate is the determined
radial profile of the formation.
FIGS. 5 to 10 show the respective contributions of the different
terms that contribute to the sensitivity function.
Specifically, FIGS. 5 & 6 shows the responses of two different
spacings. This is concerned with the geometric term of equation 1
above.
The first curve has a spacing of 0.03 m, while the second curve is
the response for a spacing of 0.10 m. It can be seen that the
second curve with the larger spacing has a peak sensitivity around
0.04 m, whereas the first curve is more sensitive at closer
distances in which the response peaks at around 0.014 m.
FIG. 6 is the integrated sensitivity of FIG. 5, which in effect
shows that by combining the responses of the different spacing
measurements, it is possible for the tool to look at different
volumes of the formation.
Thus the advantage of combining different spacings is that a wider
range of sensitivity is offered by the tool, both nearer to the
tool (i.e. borehall wall) as well as at distance further into the
formation.
FIG. 7 shows the respective contributions of the logging tool using
different frequencies for measuring the response. This is
specifically concerned with the skin depth term of Equation 1. FIG.
8 is a normalized view of the response shown in FIG. 7, which again
indicates the ability of the logging tool to be sensitive to
slightly different volumes in the formation depending on the
frequency used. The use of different frequencies allows the ability
to probe (or scan) different depths of investigation of the
formation and when combined advantageously offers an improved
radial profile of the formation. Specifically, the 10 Mhz curve is
able to see deeper into the formation, whereas the area between the
two curves shows the extra volume seen by the logging tool as a
result of the use of a different frequency.
FIG. 9 shows the combination of the geometric factor, skin depth
and wave effect terms for two different frequencies. FIG. 10 is a
normalized view of FIG. 9. FIGS. 9 and 10 show that at the higher
frequency (1 GHz) the response is more oscillatory then at the
lower frequency (10 MHz). This is important since the lower
frequency simplifies the processing needed and allows an easier
inversion calculation for determining the characteristics of the
formation.
The logging tool also has the ability to focus the EM radiation
wave in a longitudinal or transverse orientation with respect to
the tool face with appropriate focusing means (not shown). That is,
according to one embodiment, two collocated orthogonal strips are
collocated in the antenna cavity of each transmitter and can be
selectively energized by a power source for obtaining the different
transverse and longitudinal polarizations.
FIGS. 11 and 12 show top views of the respective polarizations
where a portion of the borehole 110 (borehole wall not represented)
is seen from above and the logging tool is assumed to be positioned
adjacent the arc of the borehole wall. FIG. 11 shows a longitudinal
polarization wherein the EM radiation pattern can be seen to scan a
wider horizontal volume of the formation as compared to the
transverse polarization of FIG. 12. FIG. 12 shows a transverse
polarization in which the EM radiation pattern is focused more
narrowly into the formation and shallower than the longitudinal
polarization for further depth of investigation into the
formation.
Thus, the logging tool is capable using the two different
polarizations, longitudinal and transverse, in either a combined
manner for a radial definition in the case of an isotropic
(homogenous) formation, or to allow inversion for anisotropy in
each layer in case of anisotropic formation.
Thus, it should be understood from equation 1 and FIGS. 5 to 12
that by varying the frequency, spacing and polarization of the
logging tool, and more importantly by combining at least some of
these measurements simultaneously, the logging tool offers great
sensitivity over a broader range of measurement into the formation.
By combining all three, i.e. using a plurality of different
frequency, spacing and polarization measurements simultaneously,
the optimal radial information of the formation can be obtained by
the logging tool. However, in such a case, processing times might
be longer in simultaneously combining the different measurements,
but there is advantageously described the use of a lower frequency
which might simplify such combined processing.
Furthermore, it possible to alleviating the processing requirements
by selecting the underlying model to be used for processing the
measurements in order to characterize the formation. A first model
is the so-called `electromagnetic model` (EM Model) as shown in
FIG. 13, whereas the preferred model is the so-called
`petrophysical model` shown in FIG. 14. In brief, the advantage of
the petrophysical model is that its outputs, the water conductivity
.sigma..sub.w and water saturation S.sub.w are directly computed
parameters of the formation that are required. Thus, unlike the EM
Model no further processing iteration steps (i.e. inversions) are
required to arrive at the desired parameters for characterizing the
formation. A further difference is that for the EM model, the
measurement frequencies used for each layer are independent,
whereas for the petrophysical model the frequencies of the
respective layers are linked.
More specifically, the EM model is a version of the standard FM
model, which is used to model the tool response for a given set of
permittivity .di-elect cons. and conductivity .sigma. in each
layer. In the EM model the measurement frequencies used are
independent and not linked, whereas the geometric parameters are
common FIG. 13 shows the EM model having different layers of the
radial profile, which for example are defined as: a mudcake layer
at a distance h from the borehole wall (i.e. standoff), a flushed
layer up to a distance r1 from the mudcake layer, a true layer
starting at a distance r2 from the mudcake layer and a transition
layer between the flushed and true layers. For each of these layers
it is possible to determine the tool response in term of
attenuation and phase shift using the general equation:
Amp+iPha=FM(h,r1,r2,.di-elect
cons..sub.standoff.sup.Fi,.sigma..sub.standoff,.di-elect
cons..sub.mudcake.sup.Fi,.di-elect
cons..sub.flushed.sup.Fi,.sigma..sub.flushed . . . ) Equation 3
An example of such a model is the plane mudcake model where the pad
is considered as an infinite plane. The magnetic field at receiver
for longitudinally polarized transmitter and receiver reads
.function..times..times..times..times.I.times..times..pi..times..intg..in-
fin..infin..times.d.rho..times..rho..function..times..function..times..tim-
es..rho..times.e.times..times..times..times..times..times..times..times..t-
imes..times..function..rho..times..times..function..times..times..rho..tim-
es.e.times..times..times..times..times..times..times..times..times..times.-
.function..rho..times..rho..times..times..function..times..times..rho..tim-
es.e.times..times..times..times..times..times..times..times..times..times.-
.times..times..times..function..rho..times..rho..times.
##EQU00004## where k.sub.mc, k.sub.form are the mudcake and
formation propagation constants, h.sub.mc is the mudcake thickness
and k.sub.mc,z= {square root over
(k.sub.mc.sup.2-k.sub..rho..sup.2)}{tilde over (R)}.sup.TE and
{tilde over (R)}.sup.TM are TE and TM plane wave reflection
coefficients.
The advantages of this model are: Only geometrical assumptions
Inversion output are input for petrophysical model
The following FIGS. 15 and 16 describe an example of processing
using the EM model and its robustness to noise on the data.
In the example, the logging tool is capable of using all magnetic
spacings in either differential or non-differential (single-spaced)
modes, with all polarizations and at three different frequencies.
The formation is isotropic. At each thickness step, the noise
corresponds to the thermal background noise typical from the
logging tool. In this example, the flushed zone is called shallow
zone, there is no transition zone, and the true zone is called deep
zone. The deep zone corresponds to a 10% water saturation 30 pu
sandstone, with 5 ppkk water salinity. The shallow zone corresponds
to 40% water saturation with 20 ppk filtrate salinity. Hence
shallow zone permittivity and conductivity are higher than deep
zone ones.
FIG. 15 shoes the inversion results for geometrical parameters (hmc
for mudcake, hsh for shallow zone, black are the true values, red
the inverted ones) and inversion mismatch. The measurement response
can be seen to be weakly sensitive to very small mudcake, lower
than 0.07 inch.
The mudcake thickness is not correctly reconstructed in the small
mudcake zone, but the resulting deep zone properties are not
affected as shown in FIG. 16.
Similarly on FIG. 16, the measurements are not highly sensitive to
the shallow zone electromagnetic properties for small shallow zone
thickness (h.sub.sh). However the shallow zone thickness is
reconstructed, as well as the deep zone EM properties. For shallow
zone thickness larger than 3.5 inches, the measurements are no very
sensitive to the deep zone. The reconstructed deep parameters and
shallow zone thickness suffer from the noise.
This is enlightened by the mismatch value that passes the unit
value, which is the limit of reconstruction below noise threshold.
However, the a priori information that was entered in the present
inversion was independent of the previous step. If we use the
previous step information to initialize and set an a priori on the
next value, we can improve the results. That is the choice to be
made with real data, where formation properties should vary slowly
with respect to the tool sampling rate. The mismatch value is an
indication of closely the inverted results match those from the
actual logging tool measurement, whereas the a priori value is what
is used as an initial guess. An inversion is performed to select
the optimized parameters, i.e. the model parameters that provide
results that are closest to the actual logging tool data. More
generally, the mismatch value is an indication of how coherent the
measured data are as compared with the properties computed
Note that the different spatial responses for different frequencies
and spacing are clearly visible in EM model parameter inversion
results. In black are the inversion results for shallow and deep
zones that overlap the expected values in green (dashed for the
shallow zone, solid for the deep zone). Apparent (single spacing
measurement) color coding is blue for spacing 1, (nearest), cyan,
magenta and red for spacing 4. Plain lines are for longitudinal
`apparents`, while dashed lines are for transverse `apparents`. The
apparents are a single spacing that can be used to derive
permittivity and conductivity assuming a homogeneous medium in
front of the pad (no layering). Hence the shortened name
`apparent`, since every spacing, polarization and frequency can be
used to extract apparent permittivity and conductivity values.
Thus, for a given frequency, if all apparent measurements overlap
then the formation is fully homogeneous and no layering is
present.
A petrophysical model links the different frequencies. FIG. 17
shows how the petrophysical model is able to combine the different
frequencies for each layer/zone and to derive the water
conductivity .sigma..sub.w, the water saturation S.sub.w and
eventually other formation parameters directly.
The model parameters are petrophysical parameters as water
saturation and water conductivity in each layer. The model
generically reads:
Amp+iPha=FM(.sigma..sub.mud,h.sub.standoff,.phi..sub.mudcake,h.sub.mudcak-
e,.phi..sub.rock,S.sub.water,flushed,h.sub.flushed . . . ) Equation
4
The geometrical underlying model is the same as for the EM model,
but we add a petrophysical model that relates the electromagnetic
properties of each layer to the petrophysical properties. An
example of such a model is the CRIM, Complex Refractive Index Model
that reads .di-elect cons.*=((1-.phi..sub.T) {square root over
(.di-elect cons..sub.matrix)}+.phi..sub.T(S.sub.w {square root over
(.di-elect cons..sub.water*)}+(1-S.sub.w) {square root over
(.di-elect cons..sub.oil)})).sup.2, where .di-elect cons.* is the
electromagnetic properties for a layer that has a total porosity of
.phi..sub.T and water saturation S.sub.w. The matrix permittivity
is .di-elect cons..sub.matrix and the water permittivity that
depends on the water conductivity .sigma..sub.w is .di-elect
cons..sub.water*.
The advantages of this model are: Optimization of information
Possibility of petrophysical radial profiles (salt annulus)
FIG. 18 shows the results from processing using a petrophysical
model on a field log when using r1=r2 (step response). FIG. 18
shows the solving of the formation properties: hmc, r1,
.sigma..sub.wsh, S.sub.wsh, .sigma..sub.wdeep, S.sub.wdeep (on the
header SXO_ADT: shallow and SW_ADT: deep). Using Archies equation
on the shallow and deep zone one can compute the deep resistivity
and the shallow resistivity. These are then compared to other tools
that actually measure these properties directly (RLA5 for deep
resistivity and MCFL for shallow resistivity). Specifically, it is
the moveable hydrocarbon shaded in the yellow column of FIG. 18
that displays these properties to the user (or geologist).
It should be appreciated that each of the layers of the model can
be setup according to predetermined depths into the formation. By
setting these predetermined depths to be relatively small, a
greater number of `thin` layers are used in the model. Eventually
the layers can become thin enough to be substantially equivalent to
modeling a continuous radial profile.
In a further embodiment it is advantageously possible for the
logging tool to provide better resolution of the very shallow zone
(for example, the stand-off and/or mudcake layers), which is based
on a single transmitter to a single receiver measurement, i.e. an
absolute measurement based on a single-spaced transmitter-receiver
pair.
FIG. 19 shows a standard differential measurement performed by the
logging tool, in which four measurements are combined, but they
correspond to only two different transmitter-receiver spacings.
Thus, the standard differential measurement of FIG. 19 relies on
each receiver measuring the difference from different transmitters
and then averaging the result, thereby compensating for the gain.
In contrast, the non-differential measurements of FIGS. 20 and 21
rely on single-spaced absolute measurements in which the gains need
to be compensated for. The advantage of the non-differential
measurements is that they provide improved measurement sensitivity
for shallower depths of investigation into the formation (i.e.
mudcake).
More specifically, FIG. 20 shows a non-differential measurement
(also called single-spacing) being performed in which any single
spacing transmitter-receiver pair can be used. In the example of
FIG. 20, there are two single-spacing transmit-receiver pairs used.
The first single-spacing pair comprises transmitter T.sub.A and
receiver R.sub.A, while the second single-spacing pair comprises
transmitter T.sub.B and receiver R.sub.B. It should be appreciated
that any pair, of the array of transmitters and receivers mounted
on the pad of the logging tool 2 as shown in FIG. 3, can be
selected for defining a single-spacing measurement. There are two
special cases: i) When the single-spacing method of FIG. 20 for
each receiver, in which case it is necessary to know the gain of
each transmitter-receiver pair. In this case, the vertical
resolution of the single-spacing measurements depend on each
spacing, and ii) When the single-spacing method of FIG. 20 is used
for the nearest spacing and to iteratively add the differential
gain-free measurement to obtain single spacing measurements. This
case only requires the knowledge of the nearest
transmitter-receiver gain. The vertical resolutions of the
corresponding single spacing measurements are roughly that of the
nearest single spacing measurement, because the differential
measurements are centered as shown in the example of FIG. 21.
Specifically FIG. 21 shows a further embodiment which uses two
single-spacing measurements using differential measurement minus
single-spacing nearest measurement.
Thus, while the non-differential measurement offer improved
resolution of the radial profile at shallower depths of
investigation in the formation, there is the issue of the coupled
gain of the single-spaced transmitter-receiver pair that needs to
be taken into account. This can be determined by either calibrating
during manufacturing, which depends on the temperate calibrated for
the tool, or for each log, sections of known formation properties
are selected. In the latter case, these sections can use the
differential gain-free measurements to calculate the expected
single spacing measurement values. The transmitter-receiver gains
are then evaluated by comparing the expected values from out
models, and the measured values. These measurements are made over
several consecutive depth samples, and the effective gains are then
fitted from the sample gains distributions.
FIG. 22 shows the improved estimate of the thickness of the mudcake
layer. Specifically, the `bhc` curve (representing standard
differential measurements) shows a great deal of noise over the
lower portions of the graph relative to the `abs` curve
(representing the non-differential measurement). This reduced noise
results in the advantage of increased radial definition for the
thin region in the formation closest to the pad.
A further advantage of the single-spacing measurement is to
maintain high sensitivity in an anisotropic formation, which is
lost at high frequency using differential measurement. An
anisotropic formation having different horizontal and vertical
characteristics in the formation, wherein because of the
subtraction and averaging operations performed by the differential
measurements, sensitivity is lost for these types of formations.
However, since the single-spacing (or non-differential) measurement
does not perform such operations and instead relies on an absolute
direct measurement, sensitivity is retained.
Moreover, since the logging tool is capable of using longitudinal
and transverse polarization, a further advantage is the increased
sensitivity obtained for measurement of an anisotropic formation
that is not homogenous in all orientations.
While the EM and petrophysical models can be used to model the
radial definition of the formation, according to a further
embodiment improved processing by the logging tool can be achieved
by selecting the most appropriate model for the logging tool
itself. Specifically, it is desirable to select a model that is
most suitable for inversion purposes. Inversion is the name given
to the processing concerned with the extraction of the relevant
formation properties from the measured attenuation and phase
parameters of the propagated EM waves. Such formation properties
can be expressed as either shown in equations 1, 2 or 4; b (the
forward model, EM model or petrophysical model respectively).
In order to perform this inversion from the measure responses, it
is necessary to apply a model of the logic tool itself. A first
option involves using a so-called `plane` model in which the pad of
the logging tool is modeled as a flat infinite plane aligned
alongside the borehole wall as shown in FIG. 23. The advantage of
the plane model is that because it makes such a rough
approximation, the processing is very fast to compute and hence is
particularly suitable for inversion purposes. However, it is not an
accurate model for the pad.
In contrast, it is possible to model the logging tool as a
cylindrical pad as shown in FIG. 24. This cylindrical model more
accurately reproduces the characteristics of the pad, but the
inversion processing involved with this cylindrical model is
several orders of magnitude more time consuming than for the plane
model.
To illustrate the difference of computing time required by this
model with respect to the plane model, the magnetic field
expressions are now compared.
For the plane model, consider a form expression for the plane model
homogeneous formation, in longitudinal polarization, for a
transmitter-receiver distance d and a formation propagation
constant k:
.function.I.times..times..pi..times..intg..infin..infin..times.d.rho..tim-
es..rho..function..rho..times..function..rho..times..rho..times..times..fu-
nction..rho..times..rho..times. ##EQU00005##
In the above expression, k.sub.z= {square root over
(k.sup.2-k.sub..rho..sup.2)} and H.sub.n.sup.(1) are the Hankel
function of the first kind, of order n. For a given frequency and
transmitter-receiver spacing d, it is possible to define a fixed
integration path in the complex k.sub..rho. plane and pre-compute
the Hankel functions. For each subsequent call to the function, the
integration only consists in summing these pre-computed Hankel
functions with different coefficients that are simple functions of
the formation properties and k.sub..rho.. In case of radial
layering, the coefficients remain simple functions of layers
properties and k.sub..rho..
For the cylindrical pad model, the field expression is reproduced
below with the same notation as above, with additional L.sub.mud
for the mud propagation constant, and e the eccentricity between
borehole and tool centers:
.function.I.times..times..pi..times..infin..times..times..chi..times..int-
g..infin..infin..times.d.times.eI.times..times..times..times..times.I.pi..-
times..times..rho..times..times..rho..times..function..rho..times.'.functi-
on..rho..times. ##EQU00006## where .chi..sub.n, is the Neumann
factor that is equal to 1/2 when n=0 and 1 for other n values; a is
pad radius and .alpha..sub.22n.sup.z are bottom/right elements of
the matrix solutions .sub.n.sup.z of the infinite dimension matrix
system:
.infin..infin..times..zeta..function..times..times..times..infin..infin..-
times..zeta..times..di-elect cons..infin..infin. ##EQU00007## where
.zeta..sub.m-n=J.sub.m-n(k.sub.mud,.rho.e) are eccentering factors
with Bessel functions; R.sub.m.sup.mud,form are the cylindrical
reflection coefficient matrix at borehole/formation interface that
mix TE and TM waves; R.sub.n.sup.mud,pad are the cylindrical
reflection coefficient matrix at borehole/pad interface;
s.sub.n.sup.z are source strength matrices that depend on the
source definition.
The main reasons why the cylindrical model requires more time
consuming processing are: 1. Explicit dependency of formation or
borehole variables in the different Hankel functions; hence no
pre-computation of the latter is possible. 2. For each k.sub.z on
the integration path, an infinite dimension system, with unknown
matrix coefficients that are complex function of borehole and
formation properties is necessary. The system is not always
well-conditioned; especially when the eccentricity is large and the
mode are mixing on interfaces.
The flowchart shows in FIG. 25 describes an embodiment for
implementing a pad projection model, which advantageously offers
the speed benefits of the plane model and the accuracy of the pad
model. The pad projection model comprises the steps shown within
the rectangle 260.
Specifically, at step 250 the attenuation and phase shift are
determined based on combining a plurality of measurement responses
at different spacings, polarizations and frequencies. Step 252 is
the first step of the pad projection model in which a basic
inversion is made using a pad model, but the complex processing is
overcome of the pad model is overcoming by rather using a table
(for example a look-up table) with pre-determined and finite
formation parameters. For example, five parameters are stored in
the table, i.e. permittivity and conductivity of formation,
permittivity and conductivity of mud, borehole size. These
parameters can be measured by calibration in the laboratory.
At step 254, the assumption is made that the apparent permittivity
and conductivity of the plane model is substantially similar to the
apparent permittivity and conductivity of the pad model for a
homogenous formation and pad plane. This implies that when taking
the apparent permittivity and conductivity computed from the real
pad using a homogeneous model for the formation outside the
borehole at step S254, then if a forward homogeneous plane model is
used at step S256, it is possible to obtain the projected
attenuation and phase shift parameters at step S258. These
projected parameters can then be extracted using a plane model
radial inversion at step S262 to obtain the extracted radial
permittivity and conductivity features of the formation.
The alternative branch of the flow chart with block 264 shows the
more computationally intensive pad model being used for
inversion.
The error on the result from the pad projection method is linked
directly to the error on the similarity assumption and can be
estimated a priori. FIGS. 26 and 27 are examples of apparent
permittivity and conductivity "similarity" between the plane model
and the pad model.
Specifically, FIG. 26 shows an example of an apparent permittivity
comparison between plane and pad models at: 1 GHz; deep zone
permittivity is 11 conductivity 0.1 S/m; shallow zone permittivity
is 15, conductivity is 0.5 S/m; mud permittivity is 60,
conductivity 3.5 S/m; bit size is 8.5 in. plain line is plane
model, dashed line is pad model. FIG. 27 shows an example of an
apparent conductivity comparison between plane and pad models at: 1
GHz deep zone permittivity is 11 conductivity 0.1 S/m; shallow zone
permittivity is 15, conductivity is 0.5 S/m; mud permittivity is
60, conductivity 3.5 S/m; bit size is 8.5 in.
Therefore, the projected pad model embodiment is advantageous in
not only providing an improved accuracy of the radial profile at
faster processing times, but also in providing the geologist (or
user) with a reliable indication of the accuracy of said output
results.
For accurate formation evaluation a geologist additionally would
like to know where there are so-called fractures in the rock
formation, since these fractures typically contain the hydrocarbons
sought. Standard logging tools are sufficient to pick the fracture,
but it would be desirable to have a logging tool which is able to
better characterize (or measure) the dimensions (i.e. thickness) of
such fractures in order to decide in which direction to drill.
Two different embodiments are described for determining the
fracture dimensions, one of which is best suited detecting larger
fracture dimensions and the other better suited for smaller
fracture dimensions.
When the fracture size is larger than a threshold value, for
example 0.4 inches, the logging tool in a one embodiment is
arranged to make use of the previously described idea of
single-spacing or absolute response measurement between a single
transmitter and receiver. It should be appreciated that when the
logging tool is passed over a particular formation, a flat response
will be measured when a fracture in the formation is located
between a transmitter and receiver that are coupled to form a
single-spaced pair. Thus, a flat response not only indicates that a
fracture is present, but from a single-spaced response it is
possible to estimate the location, dimensions and content of the
fracture.
Specifically, the thickness of the fracture can be estimated by
knowledge of the geometrical spacing between the
transmitter-receiver pair (i.e. the array geometry) and the tool
vertical resolution, for example d1 as defined with respect to FIG.
3.
Thus, according to one embodiment it is possible to detect the
fracture, estimate the fracture thickness as a function of the tool
vertical resolution and on the array geometry itself, and to
estimate the properties of the "substance" (or materials) contained
in the fracture itself, which is a function of the array geometry
and of the properties of the measured EM signal when a thin
fracture is crossed.
FIG. 28 shows a fracture being detected (black solid) line in the
centre between the flat responses associated with a plurality of
single-spaced transmitter-receiver pairs at a plurality of
frequencies. FIG. 29 shows a further embodiment in which the
fracture thickness can be determined with a symmetrical
transmitter-receiver single-spacing arrangement in which D1 is the
distance between transmitter plus the fracture thickness. FIG. 30
shows yet a further embodiment of determining the fracture
thickness with an asymmetrical transmitter-receiver single-spacing
arrangement in which D2 is directly the thickness of the aperture.
It is advantageous to perform both of the embodiments in FIGS. 29
and 30 and then to average the results for all spacing, frequencies
and polarization to achieve optimal results.
A further embodiment for determining the fracture dimensions is
best suited when the fraction thickness .delta. is small and is
approximated using Equation 5: H.sub.zz(d,.di-elect
cons..sub.bkg*,.di-elect
cons..sub.frac*,.delta.).apprxeq.H.sub.zz(d,.di-elect
cons..sub.bkg*)[1+.delta.(.di-elect cons..sub.frac-.di-elect
cons..sub.bkg*)H.sub.zz(d,.di-elect cons..sub.bkg*)] which in terms
of permittivity and conductivity is: .di-elect
cons..sub.zz.sup.*means.apprxeq..di-elect
cons..sub.zz.sup.*bkg+.delta.(.di-elect cons..sub.frac*-.di-elect
cons..sub.bkg*){circumflex over (.di-elect cons.)}.sub.zz.sup.*bkg
Equation 6
Hence for the apparent permittivity and conductivity, there is
determined a linear dependency on the fracture thickness .delta. as
shown for example in FIGS. 31 and 32, wherein the slope is linear
up to almost 0.8 inches, i.e. fracture of a small thickness. In
these two figures, the background is the same, but the fracture
properties are different.
For those two examples, it is possible to back-compute {circumflex
over (.di-elect cons.)}.sub.zz.sup.bkg when the slope is linear and
to check that these values obtained are the same.
The flow chart shown in FIG. 23 describes the processing steps for
determining the thickness of a small fracture .delta. providing the
sampling rate is small enough. Moreover, by using all possible
spacing of the ADT tool, the error is reduced.
In a second step, if there is available a reliable estimate of the
background medium it is possible to estimate the actual fracture
properties. The background medium is defined by the parameter
.di-elect cons..sub.bkg* and is the medium that surrounds the
fracture. In FIG. 29, the real part of the background permittivity
would be 17.3. The fracture properties comprise the real and
imaginary parts of .di-elect cons..sub.frac*. By taking an accurate
estimate of .di-elect cons..sub.bkg*, it is possible to compute the
slope {circumflex over (.di-elect cons.)}.sub.zz.sup.*bkg. Then if
.delta. has been obtained, it can be used in Equation 6 to
determine .di-elect cons..sub.frac*.
The transverse polarization shows the same behavior, but the
residual function H.sub..perp. does also depend on the fracture
properties. Thus transverse polarization can still be used to
constrain .delta.. That is, contrary to the zz case, {circumflex
over (.di-elect cons.)}.sub.zz.sup.*bkg also depends on .di-elect
cons..sub.frac*, so the slope cannot be evaluated from .di-elect
cons..sub.bkg* alone. .di-elect cons..sub.frac* cannot be estimated
from Equation 6 using the transverse polarization. However, the
geometrical behavior is the same as for zz, hence the possible
contribution to estimate .delta..
The same method can be applied for the detection and measurement of
dip when present. Dip is the left\right inclination of a bed
transverse to the pad of the logging tool. In this situation, the
constant values are a combination of longitudinal and transverse
measurement for a given transmitter polarization. Hence, combining
the direct and cross measurements allow for resolving an additional
parameter which is the dip of the fracture. FIG. 34 presents an
example of raw direct and cross measurements amplitude. A
combination of these different amplitudes with dip angle as
parameter allows retrieval of the amplitudes as shown in FIG. 35.
That is, FIG. 34 shows direct (longitudinal in plain and transverse
in dashed-dot) and cross (dashed) TA-RA[1-4] amplitude measurements
in which due to the reciprocity principle, crosses have the same
values when the fracture is in-between the transmitter and
receiver. Dip is 45 deg. FIG. 35 shown direct (longitudinal in
plain and transverse in dashed-dot) transmitter-receiver
measurements for amplitude without dip.
Yet a further method for detecting a fracture is by monitoring a
transmitter imbalance and comparing the two longitudinal and
transverse polarizations. That is, a fracture will induce a
symmetrical, but opposite phase, imbalance for the two
polarizations, wherein all imbalances happen to cross the zero line
at the middle of the fracture. FIG. 36 shows graphs reflecting
imbalance pattern in the presence of a fracture.
According to yet a further embodiment it is desirable to detect
inclusions (solids) or pebbles (or vugs) that exist in a formation
and affect the measurement of the logging tool depending on the
polarization. By combing the transverse polarization measurement of
FIG. 12 and the longitudinal polarization measurement of FIG. 11,
improved detection of such inclusions is possible since a broader
range of scanning is possible. That is, each of FIGS. 11 and 12
show a plurality of different EM waves irradiating the formation,
and wherein the longitudinal polarization which is more sensitive
to inclusions near the borehole wall contrasts with transverse
polarization front formation to form geological patterns. These
patterns are observed and gather in pattern lists for further
qualitative recognition. Inversion is also possible provided that
the observed pattern can be modeled.
Specifically, FIG. 37 shows how inclusions are detected by
combining the longitudinal and transverse polarizations, wherein
the longitudinal polarazitions scans a wider cross-sectional
horizontal volume of the formation compared to the transverse and
wherein the longitudinal spacings are more distinct from one
another than the transverse spacings. That is, it can be seen that
the EM radiation pattern has different propagation waves that cover
a large volume with respect to each other, than as opposed to the
comparatively smaller volumes covered by respective EM radiation
waves radiating from transverse polarization.
FIG. 38 shows a log with a display that enables the detection of
non-conductive inclusions in a conglomerate formation detection. As
can be seen from the log, the extraction of the rock feature
becomes understandable. Comparing the derivatives between different
spacings or setting a threshold and a counter are some examples of
automating the process.
Finally, FIG. 39 shows a display reflecting all the improvements
made in a logging tool. Furthermore since the pad of the logging
tool has an orientation device, the features can be placed in
space. Specifically the logging tool is able to: provide improved
detection of conductive and non-conductive inclusions in the
borehole wall layers and the deeper radial layers of the borehole,
detect fractures in the borehole wall, detect dipping and formation
parameters in isotropic and anisotropic layers of the various
layers of the formation.
* * * * *